It is an important point how skewed the data are. If you share the skewness and kurtosis coefficients, perhaps a more realistic advise can be given. ANOVA can be used in large samples. But if your data are too skewed, you might consider transformation options too. You can look at "Using Multivariate Statistics" by Tabachnick & Fidell

Are we assuming that the dependent/outcome variable is measured on a scale rather than categorical?

If so, I would recommend a Kruskal-Wallis. I can provide you with some further instructions on how to carry such a test out if you need. i also agree with the above comment "Using Multivariate Statistics" is a fantastic book to use.

If you have to compare the 6 groups, all with all, the appropriate statistics are ANOVA for normally distributed data (with a post-hoc analysis) or Kruskal-Wallis for non-distributed data.

To test the normality of the data, I suggest to plot the histograms, and maybe you can perform a kolmogorof-smirnof test, or a shapiro wilk test. 

The wilcoxon sum rank test is used to compare two groups. But for six groups it is better to perform a kruskal wallis or ANOVA (to reduce type 2 errors). 

SPSS software performe easily all this kind of statistics

Good luck!

I basically agree with answers above, just to make the ANOVA assumptions straight:

Except for normal distribution (of data in each group!), you need the equality of variance in each group (homoscedasticity) and independence of measurements between groups.

You can test normality by Shapiro-Wilk, equality of variances could be tested for example by Bartlett test.

If your data violate the normality or homoscedasticity assumption, go for Kruskal-Wallis test. There is special method for multiple comparisons after K-W test, which can be easily performed in R by "kruskalmc" function from package "pgirmess".

If you have  a quantitative dependent variable and at least one categorical variable, I recommend ANOVA assuming the normality and equal variances between the grous are accomplished.

If the the assumptions are not accomplished, use Krushkal Wallis test.

Hi,

I have two things to say about this. I do not totally agree with the previous answers assuming a parametric setting. ANOVA test is a default option I guess, but it appears to me that the use of Tukey's HSD is the recommended test whenever you want to do multiple comparisons. This is for several reasons but especially because it protects against the type I error simultaneously for all the pairs (FWER protection). Besides, Tukey's HSD has many optimal properties and provides simultaneous confidence intervals for the differences among the compared pairs. There is also a lot of literature for slightly better improvements, you can have a look at the book of Hochberg and Tamari on multiple comparisons or the book multiple comparisons using R by Bretz.

The other thing is that a Shapiro test for normality is a strong one and generally will fail you. So, a normality assumption is yours as long as you think that the data are well distributed.

I'm sorry, but I do not have a good background in practice about nonparametric comparisons, but the test of Kruskal Wallis that the others mentioned seems to me as a good choice.

I hope this helps and best wishes.

The overall p-value for the hypothesis that the relationships among 6 variables has no effect on the response variable is tested with ANOVA (if normal data), otherwise Kruskal-Wallis (nonparametric). For this simple question there is no need for multiple test corrections. The Tukey's test identifies which of the 6 variables contribute significantly to the effect on the response variable. This test controls for the multiple comparisons and is very important to see the extent of each of effect of each variable (xi, i=1...6) on the response variable (y).

There is no doubt that if what you are looking for is merely the effect of each of the covariables on the response, there is no need for Tukey's test because we only need to test beta_i = 0. However, if you are hoping to compare among the 6 groups, the problem is with certainly a multiple comparison. The way I understood the question is that Anand wants to compare the six groups together and not know their effect one by one with respect to the response.

Thank you everyone for you valuable contribution. Just a conclusion based on everyone's contribution and from reading some literature:

It seems like this is still a divided issue in stats. The conclusion that I can make from all your answers as well as from reading literature is that the researcher has to make a decision based on an educated guess. One comment here (and from some elsewhere) suggested that I look at the degree of skewness and make a decision based on that. If only slightly skewed, the ANOVA is robust enough to tolerate a slight skew especially with a large sample size. However, different sample sizes between the groups can reduce the ANOVA's power considerably - which unfortunately is the situation that I am in. Hence, I am now more inclined to the non-parametric Kruskal-Wallis with Post-Hoc Scheffe Test.

However, I did run several extensive test for normality, to have a better view of the data's distribution namely Shapiro test, Skewness test, Kurtosis test, Q-Q plot, Levene's test, Brown-Forsythe test and the new non-parametric Levene's test. All these test shows that my data is heavily skewed, kurtotic and heteroscedastic. For trial, I did apply a Log transformation that some researcher suggested (which I do not agree with) which resulted in the data still being non-normal.

Based on this situation, I think I will stick to the non-parametric approach for now despite having a large samples size.

Thank you all once again for you valuable advice!

Well done!

Dear Anand Nainar

Please check this article, it will help you in that

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